Least Common Multiple (LCM) of 126 and 157
The least common multiple (LCM) of 126 and 157 is 19782.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 126 and 157?
First, calculate the GCD of 126 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 157 = 0 remainder 126 |
| 2 | 157 ÷ 126 = 1 remainder 31 |
| 3 | 126 ÷ 31 = 4 remainder 2 |
| 4 | 31 ÷ 2 = 15 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 164 | 23452 |
| 68 and 141 | 9588 |
| 132 and 114 | 2508 |
| 136 and 21 | 2856 |
| 179 and 83 | 14857 |